Plenty of good speakers at $300 though.
I have said this in other threads and will say it again, if you are really interested in the price/performance equasion dont even think about wasting money below $500. That sort of budget you can buy a reasonable quality amp and some nice bookshelfs AND MOST IMPORTANTLY a dedicated USB DAC. Entry level system for anyone interested in sound quality will throw the laptop soundcard away simply due to internal noise and will invest 1/3rd of the budget into a USB DAC by fiio/ibasso/other. Even a dedicated audio device from focusrite or m-audio will blow you internal DAC away, and would not break the bank. From there you know you are getting a sound worth amplifying, and you can choose how you go about it. If you choose active then your remaining 2/3rds goes on active monitors/sub or if you choose the passive route split you budget almost down the middle for AMP and speakers. From my perspective $300 is not going to achieve a good outcome and you are "almost" throwing money away and may as well get a crappy $100 external speaker for your laptop. Double your budget to maybr $600 and you will EASILY appreciate the difference.
Many people like to tell you how to spend your money, and I may seem like that kind of person, I am just trying to put accross that you may regret the path you look to be taking. Your source is a laptop and that is far from ideal without carefully planning how you get the data and turn it into sound. In general terms I also tend to agree with Active Man regarding amp/driver synergy. An amp is designed to make a clean sound at a set output, which is not always ideal for the passive speakers you buy. When you buy an active monitor the drivers and amplification are carefully matched and are pretested so that you know they are working with each other.
I would suggest you do some reading on fiio USB DAC's, there are other brands but fiio are widely distributed, then move on to looking into some active monitors from Behringer/Focal/KRK from there you can always save a little longer and add a sub.
HTH and good luck.
At this price point I would recommend any offering of Q-Acoustics. In particular the new 2020i, which gets a good review from what-hifi.
At work we sell these a lot to people. I too would recommend to stretch the budget a little bit and get better gear. $300 would only barely
cover the speakers.
@ImperiumDX, have you tried the Q-Acoustics 2020i and the Audioengine P4? How do the two passive speakers compare? Thanks!